Later June would probably be better than early June. Although, there have been years where I've seen scorching sunny weather in early june, then crappy weather all summer. You just never know what you'll get around here.
If we're talking about this year, the third Saturday, the 18th would be good for me. Otherwise maybe the third or fourth Saturday of June for future years.
We could conclude our meet-up with a short ride to Royal Enfield Seattle. It's just over the Freemont bridge, and around the zoo to the other side. Probably about a mile. Hwy 99 is right there, and I-5 is close too, for departures.
Another Idea is a group ride around Magnolia. I was just told about it last Sunday. Nice roads with minimal traffic, sweeping views from the bluff. It's my next destination to explore.